Restricted function-on-function linear regression model.

Area of Science:

• Statistics
• Functional Data Analysis
• Regression Modeling

Background:

• Standard function-on-function linear regression assumes predictor curves influence response curves across the entire domain.
• Real-world scenarios often involve localized influences, such as historical or short-term associations, not captured by traditional models.
• The need for models that account for subregional influences in functional data analysis is critical.

Purpose of the Study:

• To develop an accurate and computationally efficient estimation procedure for restricted function-on-function regression models with a predefined subregion.
• To propose a data-driven subregion selection method for models where the influential subregion is not known a priori.
• To enhance model interpretability and predictive performance through localized functional regression.

Main Methods:

• Development of a novel estimation algorithm for the restricted function-on-function model.
• Introduction of a subregion selection procedure to identify the most relevant part of the predictor curve.
• Algorithm implementation for both parameter estimation and subregion identification.

Main Results:

• The proposed estimation procedure offers improved accuracy and computational efficiency for the restricted model.
• The subregion selection method facilitates the identification of influential predictor curve segments.
• Algorithms are successfully developed for both estimation and selection tasks.

Conclusions:

• The restricted function-on-function regression model effectively captures localized relationships in functional data.
• The developed methods provide practical tools for accurate modeling and interpretation in functional data analysis.
• This approach enhances predictive capabilities by focusing on relevant subregions of predictor curves.